Question

Which of the following is the rational exponent expression of third root of 4 n? A) (4n)3

B) 3n4

C) quantity of 4 n to the one third power

D) 4 times n to the one third power

Answer 1

The answer to the question above should be letter "C. quantity of 4 n to the one-third power". This means that the radicand is the product of 4 and n. This product is raised to the power 1/3. Mathematically,
(4n)^1/3

Answer 2

You have to check which of the following expressions is the rational exponent expression of third root of 4n, or mathematically,
`\sqrt[3]{4n} .` Consider all cases:

A.
`(4n)^3=4^3\cdot n^3=64n^3\\eq\sqrt[3]{4n} .`

B.
`3n^4\\eq \sqrt[3]{4n} .`

C. quantity of 4n to the one third power is
`(4n)^{(1)/(3) }=\sqrt[3]{4n}` (by the definition of rational power).

D. 4 times n to the one third power is
`4\cdot n^{(1)/(3) }=4\sqrt[3]{n}\\eq \sqrt[3]{4n} .`

Answer: correct choice is C.